Profit maximization inventory model with uncertain demand and costs: a geometric programming approach

In this paper, we formulate a new profit maximization inventory model in which demand is a power function of selling price, marketing expen-diture, and service expenditure, and unit cost is a power function of order quantity. In reality, the exponents of selling price, marketing expenditure, and service expenditure in a demand function and the exponent of order quantity in a unit cost function may not be exact. So, we consider the model in an uncertain-based framework with the assumption that the exponents of selling price, marketing expenditure, and service expenditure in a demand function and the exponent of order quantity in a unit cost function are uncertain. Based on uncertainty theory, we develop a method to find the equivalent crisp model. In addition, we use the geometric programming method to solve the crisp model. Furthermore, we give a suitable numerical example to show how the proposed methodology can be used to solve the model for different uncertainty distributions at different uncertainty levels. In the numerical example, we use five different uncertainty distributions and figure out the selling price, market-ing cost, service cost, order quantity, and profit with respect to the uncertainty level for each uncertainty distribution. Finally, we perform a sensitivity anal-ysis for a better understanding of the proposed model.